contrib/oxl/mvl/Probability.cxx

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// This is oxl/mvl/Probability.cxx
#include "Probability.h"
//:
// \file

#include <vcl_cstdlib.h>
#include <vcl_vector.h>
#include <vcl_iostream.h>
#include <vcl_cassert.h>

#include <vnl/vnl_matrix.h>
#include <vnl/vnl_diag_matrix.h>
#include <vnl/vnl_math.h>

#include <mvl/HomgPoint2D.h>
#include <mvl/FMatrix.h>

//:
// Randomly select samples points from the screen size of row_size & col_size
// bucketed symmetrically with buckets partitions on the area.
// Note that no two selected points can lie in the same bucketed partition.
//
// Watch this routine, if the given points are not dispersed
// uniformly enough across the given distribution then the routine will
// not exit, rather keep searching for the requested number of subsamples.
//
// Fixed => RESCALE ALL THE POINTS TO FIT -1,1(x) -1,1(y)
// IT IS SUPPOSED THAT THE CENTER OF THE POINTS IS (0,0)

vcl_vector<int> Monte_Carlo(vcl_vector<HomgPoint2D> points, vcl_vector<int> index, int buckets, int samples)
{
  assert(samples > 0);
  double row_size = 2.0;
  double col_size = 2.0;
  vcl_vector<int> out_points(samples);
  double row_div = row_size/buckets;
  double col_div = col_size/buckets;
  int no_buckets = buckets*buckets;
  if (buckets < 1) {
    vcl_cerr << "Warning Monte Carlo sampling will not work.\n"
             << "Not enough buckets: need 1, have " << buckets << ".\n";
  }
  if (index.size() < (unsigned int)samples) {
    vcl_cerr << "Warning Monte Carlo sampling will not work.\n"
             << "Not enough points to choose from: need " << samples
             << ", have " << index.size() << ".\n";
  }

  //
  //  RESCALE AND CENTER THE POINTS
  //
  //  Store the modified points in the new list "points_rescale"
  //  for use in the test condition only
  //

  double max_x = -1e31, max_y = -1e31, min_x = 1e31, min_y = 1e31;

  for (unsigned int i=0;i<index.size();i++)
  {
    if ( points[i].x() > max_x )
      max_x = points[i].x();

    if ( points[i].y() > max_y )
      max_y = points[i].y();

    if ( points[i].x() < min_x )
      min_x = points[i].x();

    if ( points[i].y() < min_y )
      min_y = points[i].y();
  }

  double center_x = ( max_x - min_x ) * 0.5;
  double center_y = ( max_y - min_y ) * 0.5;

  vcl_vector<vnl_double_2> points_rescale;
  for (unsigned int i=0;i<index.size();i++)
  {
    vnl_double_2 v = points[i].get_double2(); // non-homogeneous representation
    double x = -1.0 + ( v[0] - min_x ) / center_x;
    double y = -1.0 + ( v[1] - min_y ) / center_y;
    points_rescale.push_back( vnl_double_2( x, y ) );
  }

  // ********************* //

  for (unsigned int i=0; i < (unsigned int)samples; )
  {
    int random;
    if (buckets > 1) {
      random  = (int)((float)(no_buckets - 1)*vcl_rand()/(RAND_MAX+1.0));
    }
    else {
      random  = 1;
    }

    int row_num;
    if (buckets > 1) {
      row_num = random/buckets;
    }
    else {
      row_num = 0;
    }
    int col_num;
    if (buckets > 1) {
      col_num = random - row_num*buckets;
    }
    else {
      col_num = 0;
    }

    double row_check_lower = row_num * row_div;
    double col_check_lower = col_num * col_div;
    double row_check_upper = row_num * row_div + row_div;
    double col_check_upper = col_num * col_div + col_div;
    row_check_lower -= 1.0;
    col_check_lower -= 1.0;
    row_check_upper -= 1.0;
    col_check_upper -= 1.0;

    vcl_vector<int> list;

    // Select from the first list
    for (unsigned int j = 0; j < index.size(); j++) {
      double x = points_rescale[j][0], y = points_rescale[j][1];
      if (y >= row_check_lower && y < row_check_upper &&
          x >= col_check_lower && x < col_check_upper) {
        list.push_back(index[j]);
      }
    }
#if 0 // was:
    for (int j = 0; j < index.size(); j++) {
      double x = points[j].x(), y = points[j].y(), w = points[j].w();
      if (w < 0) { x *= -1; y *= -1; w *= -1; }
      if (y >= row_check_lower*w && y < row_check_upper*w &&
          x >= col_check_lower*w && x < col_check_upper*w)
        list.push_back(index[j]);
    }
#endif //********************************************

    int list_size = list.size();
    bool not_picked = true;
    if (list_size != 0) {
      int counter = 0;
      bool fail;
      while (not_picked && counter < list_size*4) {
        int pick = (int)((float)(list_size - 1)*vcl_rand()/(RAND_MAX+1.0));
        int picked = list[pick];
        fail = false;
        for (unsigned int k = 0; k < i; k++) {
          if (picked == out_points[k])
            fail = true;
        }
        if (!fail) {
          out_points[i] = picked;
          not_picked = false;
          i++;
        }
        else {
          counter++;
          //vcl_cerr << "Failed\n";
        }
      }
    }
    list.clear();
  }

  return out_points;
}

#if 0 // Note : this hasn't been implemented properly yet
vcl_vector<HomgPoint2D> Taubins_MLE(HomgPoint2D x1, HomgPoint2D x2, FMatrix *F)
{
  vcl_vector<HomgPoint2D> actual_points;

  // Generate a Jacobian matrix
  vnl_matrix<double> J;
  J.put(1, 1, (F->get(1, 1) - x2*F->get(3, 1)));
  J.put(1, 2, (F->get(1, 2) - x2*F->get(3, 2)));
  J.put(1, 3, (-x*F->get(3, 1) - y*F->get(3, 2) - F->get(3, 3)));
  J.put(1, 4, 0.0);
  J.put(2, 1, (F->get(2, 1) - y_dash*F->get(3, 1)));
  J.put(2, 2, (F->get(2, 2) - y_dash*F->get(3, 2)));
  J.put(2, 3, 0.0);
  J.put(2, 4, (-x*F->get(3, 1) - y_dash*F->get(3, 2) - F->get(3, 3)));

  // Find the Moore-Penrose Pseudo Inverse for the Jacobian matrix
  vnl_svd<double> svd(J, 1e-8);
  vnl_diag_matrix<double> diag = svd.W;
  for (int i = 0; i < diag.size(); i++) {
    if (diag(i, i) != 0.0)
      diag(i, i) = 1 / diag(i, i);
  }
  vnl_matrix<double> pseudo = svd.U * diag * svd.V.transpose();

  // Find the residuals

  return actual_points;
}
#endif

double Sampsons_MLE(HomgPoint2D x1, HomgPoint2D x2, FMatrix *F)
{
  double rX, rY, rX_dash, rY_dash, GRADr, r, dist;
  vnl_matrix_fixed<double,3,3> temp = F->get_matrix();
  vcl_cerr << x2.x() << vcl_endl;
  rX = temp.get(0, 0)*x2.x() + temp.get(1, 0)*x2.y() + temp.get(2, 0);
  rY = F->get(0, 1)*x2.x() + F->get(1, 1)*x2.y() + F->get(2, 1);
  rX_dash = F->get(0, 0)*x1.x() + F->get(0, 1)*x1.y() + F->get(0, 2);
  rY_dash = F->get(1, 0)*x1.x() + F->get(1, 1)*x1.y() + F->get(1, 2);
  vcl_cerr << "Points : " << rX << ' ' << rY << ' ' << rX_dash << ' ' << rY_dash << vcl_endl;
  GRADr = vnl_math_sqr(rX*rX + rY*rY + rX_dash*rX_dash + rY_dash*rY_dash);
  vcl_cerr << "1 :  " << GRADr << vcl_endl;
  // This is an annoying interface
  HomgPoint2D *x1p = new HomgPoint2D(x1.x(), x1.y(), 1.0);
  HomgPoint2D *x2p = new HomgPoint2D(x2.x(), x2.y(), 1.0);
  vcl_cerr << "2\n";
  r = F->image1_epipolar_distance_squared(x1p, x2p);
  vcl_cerr << "r " << r << vcl_endl;
  dist = r/GRADr;
  return dist;
}